1. Field of the Invention
The present invention is related generally to the field of modeling and more particularly to a method for modeling an underground structure such as an underground storage tank.
2. Description of the Related Art
Underground storage tanks (USES) are commonly used to store a wide variety of liquids such as gasoline. A typical UST 100 is shown in FIG. 1. The UST 100 includes a plurality of ribs 110. The UST 100 shown in FIG. 1 is a double wall UST with an inner wall 120 and an outer wall 130. Single wall as well as multiple wall USES are also used. The UST 100 may also includes a man head 140 (the man head 140 will not be modeled or discussed further herein). An installed UST is typically buried in a trench which has been backfilled with material such as sand or pea gravel.
Many of the liquids stored in USES are dangerous and/or harmful if released from a UST into the ground. Given this danger, one natural concern is that a UST be strong enough to withstand a seismic event such as a major earthquake.
One method that can be used to determine whether a UST is capable of withstanding a major earthquake is to physically reproduce earthquake conditions in the vicinity of an actual UST. However, given the size of an actual UST and/or the cost of creating UST models during the design process, as well as other factors, such methods are prohibitively expensive. A natural alternative to the aforementioned methods is the use of software modeling to predict UST behavior in an earthquake. Unfortunately, an adequate method for modeling UST behavior during earthquakes does not exist until this invention.
Different areas of the U.S. are covered by one of three different building codes. Of these, the Uniform Building Code, which is used throughout much of the western part of the country, is the dominant seismic code used throughout the U.S. and much of the world. The seismic portion of the Uniform Building Code is taken primarily from the xe2x80x9cBlue Book,xe2x80x9d which is issued by the Structural Engineers Association of California. A review of the Blue Book indicates that buried structures are not considered within its scope of seismic analysis. Another recommendation for design of seismic structures comes from the Applied Technology Council, which is funded by the National Science Foundation. The recommendations provided in their set of publications do not address underground tanks except for a brief discussion in several of their publications. No methodology, however, is developed for analysis of such underground tanks during earthquakes. U.S. Department of Defense documents related to nuclear blast designs of nuclear silo sites, which would presumably be helpful, are mainly classified. Several Japanese publications have considered this problem, but have not addressed any specific issues or developed any specific methods.
The U.S. Department of Energy has provided some guidelines on the design of USES. Their methodology has generally been to provide an equivalent static pressure which is applied on the external surface of the tank. The tank wall stresses are then developed using hell-type or plate-type theory. Static methods such as these are inapplicable to a dynamic environment such as an earthquake.
Other types of buried systems are also discussed in the literature, including a variety of lifeline systems. Lifeline systems generally refer to long pipes or conduits, either filled or empty. Analysis of lifeline systems discussed in the literature always assumes that the lifeline is of infinite length with the seismic waves applied at various angles to the longitudinal axis of the lifeline. In the early 1980""s, Owens Corning developed a seismic analysis for their underground tanks utilizing such lifeline methodology. Given the aforementioned assumptions, such methodology is not adequate for analysis of USES during seismic events such as major earthquakes.
What is needed is a method for analyzing the behavior of underground structures such as USES during seismic events such as earthquakes.
The present inventions meet the aforementioned need to a great extent by providing a method for modeling an underground structure such as a DUST which uses a finite element model in which the backfill, ribs and tank shell are separately modeled and then combined into a system model of the DUST/soil system. The backfill material is modeled using three-dimensional solid (brick) elements. The tank shell is modeled using three-dimensional plate/shell elements and the rib is modeled using beam elements. Dynamic horizontal and vertical accelerations, preferably those recorded during an actual quake such as the 1994 Northridge quake in California, are then applied as forcing functions on the system model to evaluate performance of the DUST using a time-history analysis. The method is preferably performed using a commercially available finite element analysis computer program.